Applications of the Euler characteristic in bifurcation theory.

Rybicki, Slawomir. "Applications of the Euler characteristic in bifurcation theory.." Publicacions Matemàtiques 35.2 (1991): 527-535. <http://eudml.org/doc/41711>.

@article{Rybicki1991,
abstract = {Let f: Rn x Rn → Rn be a continuous map such that f(0,λ) = 0 for all λ ∈ Rk. In this article we formulate, in terms of the Euler characteristic of algebraic sets, sufficient conditions for the existence of bifurcation points of the equation f(x,λ) = 0. Moreover we apply these results in bifurcation theory to ordinary differential equations. It is worth to point out that in the last paragraph we show how to verify, by computer, the assumptions of the theorems of this paper.},
author = {Rybicki, Slawomir},
journal = {Publicacions Matemàtiques},
keywords = {bifurcation point; Euler characteristic; Brouwer equations; topological degree},
language = {eng},
number = {2},
pages = {527-535},
title = {Applications of the Euler characteristic in bifurcation theory.},
url = {http://eudml.org/doc/41711},
volume = {35},
year = {1991},
}

TY - JOUR
AU - Rybicki, Slawomir
TI - Applications of the Euler characteristic in bifurcation theory.
JO - Publicacions Matemàtiques
PY - 1991
VL - 35
IS - 2
SP - 527
EP - 535
AB - Let f: Rn x Rn → Rn be a continuous map such that f(0,λ) = 0 for all λ ∈ Rk. In this article we formulate, in terms of the Euler characteristic of algebraic sets, sufficient conditions for the existence of bifurcation points of the equation f(x,λ) = 0. Moreover we apply these results in bifurcation theory to ordinary differential equations. It is worth to point out that in the last paragraph we show how to verify, by computer, the assumptions of the theorems of this paper.
LA - eng
KW - bifurcation point; Euler characteristic; Brouwer equations; topological degree
UR - http://eudml.org/doc/41711
ER -